Mathematical Surveys and Monographs Volume: 230
2018; 231 pp; Hardcover
Print ISBN: 978-1-4704-4291-0
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the gquasithinh part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG.
The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Graduate students and researchers interested in group theory and its applications.
AMS/MAA Textbooks Volume: 39
2018; Hardcover
Print ISBN: 978-1-4704-4348-1
A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the p-adic numbers, quadratic extensions of the integers, and arithmetic generating functions.
EMS Series of Congress Reports Volume: 13
2018; 354 pp; Hardcover
Print ISBN: 978-3-03719-182-8
IMPANGA stands for the activities of Algebraic Geometers at the Institute of Mathematics, Polish Academy of Sciences, including one of the most important seminars in algebraic geometry in Poland. The topics of the lectures usually fit within the framework of complex algebraic geometry and neighboring areas of mathematics.
This volume is a collection of contributions by the participants of the conference IMPANGA 15, organized by participants of the seminar, as well as notes from the major lecture series of the seminar in the period 2010?2015. Both original research papers and self-contained expository surveys can be found here. The articles circulate around a broad range of topics within algebraic geometry such as vector bundles, Schubert varieties, degeneracy loci, homogeneous spaces, equivariant cohomology, Thom polynomials, characteristic classes, symmetric functions and polynomials, and algebraic geometry in positive characteristic.
Researchers interested in complex algebraic geometry.
Asterisque Volume: 394
2018; 110 pp; Softcover
Print ISBN: 978-2-85629-869-5
In this paper, the author proves the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane over the algebraic numbers. More precisely, f let be an endomorphism of the affine plan over the algebraic numbers. Let x be a point in the affine plan and C be a curve. If the intersection of C and the orbits of x is infinite, then C is periodic.
Graduate students and research mathematicians.
EMS Tracts in Mathematics Vol. 28
ISBN print 978-3-03719-178-1
February 2018, 379 pages, hardcover, 17 x 24 cm.
Optimizing the shape of an object to make it the most efficient, resistant, streamlined, lightest, noiseless, stealthy or the cheapest is clearly a very old task. But the recent explosion of modeling and scientific computing have given this topic new life. Many new and interesting questions have been asked. A mathematical topic was born ? shape optimization (or optimum design).
This book provides a self-contained introduction to modern mathematical approaches to shape optimization, relying only on undergraduate level prerequisite but allowing to tackle open questions in this vibrant field. The analytical and geometrical tools and methods for the study of shapes are developed. In particular, the text presents a systematic treatment of shape variations and optimization associated with the Laplace operator and the classical capacity. Emphasis is also put on differentiation with respect to domains and a FAQ on the usual topologies of domains is provided. The book ends with geometrical properties of optimal shapes, including the case where they do not exist.
Keywords: Shape optimization, optimum design, calculus of variations, variations of domains, Hausdorff convergence, continuity with respect to domains, G-convergence, shape derivative, geometry of optimal shapes, Laplace-Dirichlet problem, Neumann problem, overdetermined problems, isoperimetric inequality, capacity, potential theory, spectral theory, homogenization
IRMA Lectures in Mathematics and Theoretical Physics Vol. 28
ISBN print 978-3-03719-183-5
February 2018, 240 pages, softcover, 17 x 24 cm.
The aim of this book is to serve as an introductory text to the theory of linear forms in the logarithms of algebraic numbers, with a special emphasis on a large variety of its applications. We wish to help students and researchers to learn what is hidden inside the blackbox ?Baker's theory of linear forms in logarithms' (in complex or in p-adic logarithms) and how this theory applies to many Diophantine problems, including the e ffective resolution of Diophantine equations, the abc-conjecture, and upper bounds for the irrationality measure of some real numbers.
Written for a broad audience, this accessible and self-contained book can be used for graduate courses (some 30 exercises are supplied). Specialists will appreciate the inclusion of over 30 open problems and the rich bibliography of over 450 references.
Keywords: Baker's theory, linear form in logarithms, Diophantine equation, Thue equation, abc
-conjecture, primitive divisor, irrationality measure, p-adic analysis